Surface electromyography (sEMG) is the technique of recording electrical signals from the skin overlying muscles in order to estimate the activity in the muscle beneath. sEMG has been used in the following areas:                1. Research: to measure the activity in muscles during voluntary movement or in response to interventions that might affect muscles, motor control, or other aspects of voluntary or involuntary muscle contraction. During voluntary movement, the sEMG signal is often interpreted as the “intent” of the subject, which may be different from the resulting movement when external forces or constraints are present.        2. Biofeedback: to isolate the activity of individual muscles and provide information to the subject about the state of those muscles. Biofeedback may be used in order to increase activity and thereby strengthen weak muscles, it may be used in order to decrease activity and thereby relax dystonic muscles or muscle spasms, or it may be used to reinforce particular desired patterns of activity of multiple muscles. Biofeedback can be used both for clinical treatment and for training competitive sports.        3. Control: to use the activity of one or more muscles in order to control electromechanical devices. This has been extensively investigated for patients with limb amputations, or with neurological disorders (including spinal cord injury, amyotrophic lateral sclerosis, or stroke) that prevent normal movement. The goal in such cases is the construction of electrically-controllable prosthetic devices. One of the most extreme applications is when sEMG is combined with functional electrical stimulation (FES) so that sEMG signals from one muscle are used to stimulate the contraction of another muscle in order to reinstate some degree of control over paralyzed limbs.        
Despite the tremendous promise of sEMG technology, essentially all applications have been severely hampered by the poor quality of sEMG signals. It is generally believed that sEMG provides a “noisy” signal that is of insufficient quality for accurate control. Therefore the quality of research data is poor, use in biofeedback is limited to simple activation or deactivation of muscles, and use in control is limited to simple on-off switches that often require careful tuning and practice in order to achieve reliable performance. Strategies to improve performance have attempted to place multiple sEMG electrodes in order to reduce noise and provide more consistent signals. However, such methods have had limited success and even more limited applicability due to their complexity and the very modest improvement in signal quality.
Inspection of sEMG signals reveals the difficulty with their interpretation (see FIG. 1): the sEMO signal appears to be extremely noisy, yet the resulting force that is generated is much smoother. It seems that the level of noise in the sEMG signal reflects the resulting force much more than the actual values of the sEMG signal. This suggests that one strategy for reading the sEMG signal is to estimate the magnitude of the noise itself.
Current State of the Art
Current methods for interpreting sEMG attempt to estimate the “envelope” of the signal. This corresponds to an assumed model for the generation of sEMG as:sEMG(t)=x(t)*n(t)where at each time t the value of the sEMG signal is the product of an activity level x(t) and Gaussian white noise n(t). Estimation of x(t) is typically achieved by estimating the power in the sEMG signal, becauseE[sEMG2(t)]=E[x2(t)n2(t)]=σ2x2(t)where E[ ] indicates the expected value, σ2 is the noise variance, and x2(t) is the square of the current value of the activity level. In practice, this is usually approximated using the absolute value (the positive square root of both sides of the equation) and the expectation operator is estimated by the use of a low-pass filter. We refer to the combination of rectification (absolute value) and low-pass filtering as the “linear method”.
FIG. 2 shows another example of sEMG, the true resulting force, and the linear method estimate for several different low-pass filters. From the figure, we see several of the shortcomings of the linear method:                1. Even for very smooth filters, there is still considerable “ripple” in the estimate that is not present in the true force tracing.        2. There is a delay between the onset of sEMG and the reaction of the filter and that is even longer than the delay between sEMG and generation of muscle force.        3. There is a tradeoff between the ability of the filter to respond rapidly to sudden changes in sEMG and the ability to maintain a smooth response. In particular, filters with better responsiveness to change (upper traces) have much higher variability, while filters with lower variability (lower traces) have more sluggish response to changes in sEMG.        
The reason for the poor performance of linear filters lies in the method of estimating E[x2(t)n2(t)]. Since the sEMG signal behaves like modulated white noise, a short time interval of estimation (corresponding to a low-pass filter with higher cutoff frequency) will form a poor estimate of x(t). Yet a longer time interval of estimation (corresponding to a low-pass filter with lower cutoff frequency) will only form a good estimate of x(t) if x(t) is not changing during that interval. If x(t) is changing, then the filter itself determines the maximum achievable frequency response, and this introduces an artificial limitation on the bandwidth of the estimated signal. For example, the smoothest filter response in FIG. 2 occurs for a filter with −20dB cutoff at 1 Hz, so for this filter the output will never contain frequencies above 1 hz, even if the subject in reality is moving much more rapidly. But no matter how smooth the filter is, since the input behaves like white noise the output will behave like filtered noise and thus will remain randomly varying, even if the variation is slow.
Taking these issues into account, we see that the linear method behaves appropriately only if x(t) is unchanging or very slowly changing. Even then, the stability of the output estimate is poor. The technique proposed herein is to take into account the change in x(t) by providing an explicit model for x(t) as a stochastic process. The sEMG signal is then a version of x(t) that has been corrupted by multiplicative noise.
It is desirable to provide improved approaches, including both devices and methods, for treating and rehabilitating patients suffering from disabilities due to limb loss, muscle loss, muscle fatigue, loss of motor neuron activity, loss of neural tissue, neurological disorders, stroke, and other related conditions.